Nonnegative Matrix Pairs, 2-D Dynamical Systems and Road-Colorings

Bryan L. Shader
University of Wyoming (ILAS Speaker)

The classic Perron-Frobenius Theory shows that combinatorial, algebraic and
spectral properties of nonnegative matrices are closely related, and this powerful
tool has been successfully used in the analysis of Markov chains. The talk develops
the analogous relationships between k-tuples of n by n nonnegative matrices,
the combinatorics of colored digraphs, and the analysis of higher dimensional
dynamical systems. The techniques discussed are then applied to solve a weak
version of the famous road-coloring conjecture that arose in finite automata
and symbolic dynamics.